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1、PartIINTRODUCTIONFuzzinessisnotapriorianobviousconceptanddemandssomeexplana-tion.“Fuzziness”iswhatBlack(NF1937)calls“vagueness”?whenhedistinguishesitfrom“generality”andfrom“ambiguity.”Generalizingreferstotheapplicationofasymboltoamultiplicityofobjectsinthefieldofreference,ambiguit
2、ytotheassociationofafinitenumberofalternativemeaningshavingthesamephoneticform.But,thefuzzinessofasymbolliesinthelackofwell-definedboundariesofthesetofobjectstowhichthissymbolapplies.Morespecifically,letXbeafieldofreference,alsocalledauniverseofdiscourseoruniverseforshort,covering
3、adefiniterangeofobjects.Considerasubset?wheretransitionbetweenmembershipandnonmem-bershipisgradualratherthanabrupt.This“fuzzysubset”obviouslyhasnowell-definedboundaries.Fuzzyclassesofobjectsareoftenencounteredinreallife.Forinstance,?maybethesetoftallmeninacommunityX.Usually,therea
4、remembersofXwhoaredefinitelytall,otherswhoaredefinitelynottall,butthereexistalsoborderlinecases.Traditionally,thegradeofmembership1isassignedtotheobjectsthatcompletelybelongto?—herethemenwhoaredefinitelytall;converselytheobjectsthatdonotbelongto?atallareassignedamembershipvalue0.Q
5、uitenaturally,thegradesofmembershipoftheborderlinecasesliebetween0and1.The?However,itmustbenoticedthatZadeh(1977a)[ReferencefromIV.2]hasusedtheword“vagueness”todesignatethekindofuncertaintywhichisbothduetofuzzinessandambiguity.1www.aibbt.com艾伯特-專注人工智能FuzzySetsandSystems:TheoryandA
6、pplicationsbyDidierDuboisandHenriPradeI.Introduction2moreanelementorobjectxbelongsto?,thecloserto1isitsgradeofmembershipm(x).Theuseofanumericalscalesuchastheinterval[0,1]?allowsaconvenientrepresentationofthegradationinmembership.Precisemembershipvaluesdonotexistbythemselves,theyar
7、etendencyindicesthataresubjectivelyassignedbyanindividualoragroup.Moreover,theyarecontext-dependent.Thegradesofmembershipreflectan“ordering”oftheobjectsintheuniverse,inducedbythepredicateassociatedwith?;this“ordering,”whenitexists,ismoreimportantthanthemembershipvaluesthemselves.T
8、hemembershipassessmentofobjectsca
